How to copy keyframes from one Action to another?
Here is a script that copies actionA (hardcoded to "CubeAction", change to suit) to actionB and adds a frame offset to each key.

import bpy
# change how action is picked
# actionA = bpy.context.object.animation_data.action
actionA = bpy.data.actions.get("CubeAction")
if actionA is not None:
    # copy the action
    actionB = actionA.copy()
    offset = 10 # frames
    # iter thru fcurves and move keyframes by offset
    for fc in actionB.fcurves:
        for kf in fc.keyframe_points:
            kf.co.x += offset


Note this can also be done pretty simply in the NLA, by moving an action strip to the desired frame start.  This way you can keep all your actions as starting at frame 1.